Elysia was governed by the Elysian Council. Its "starship graveyard" contained all of the ships lost in the Delta Triangle over the millennium preceding the arrival of the USS Enterprise. While time passed at the same rate, the effects of time, like aging, occurred at an extremely slow rate in Elysia relative to the outside universe. All acts of violence were forbidden in Elysia, and were stopped by the members of species with psionic powers. CaptainJames T. Kirk noted that "Elysia is, in many respects, a perfect society. But with all its virtues, it is not home. And home, with all its faults, is where we prefer to be." (TAS: "The Time Trap")

According to the Star Trek: Department of Temporal Investigations novel Forgotten History the "time standing still" in Elysia was an effect caused by actions requiring less energy there. This caused aging to be slower and healing mechanisms to be more effective. It was also theorized this effect might even be responsible for the more peaceful society, because even thoughts took less effort, making it easier to come up with better solutions.